On additive property of finitely additive measures

2019/05/22 by Kunisada, Ryoichi
#28E10 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · doi:10.48550/arxiv.1905.09206

Abstract

By the additive property, we mean a condition under which L^p spaces over finitely additive measures are complete. Basile and Rao gives a necessary and sufficient condition that a finite sum of finitely additive measures has the additive property. We generalize this result to the case of a countable sum of finitely additive meaures. An application of this result to density measures are also presented.

Related

• Density measures and additive property
• Measures on Boolean algebras
• Finitely additive measures on Boolean algebras
• Uniform measures and countably additive measures
• Algebraic characterizations of measure algebras